Finite Group Databasebeta

← #49094307

Subgroups — #49094307

Order 35968.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31824040C211yesmaximal, characteristic
2#31823777C211yesmaximal, characteristic, complemented
3#31823774C211yesmaximal, characteristic, complemented
4#31823395C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9#22582857—21no—
10#22582856—21no—
11#22582853C2211yescharacteristic
12#22582852—21no—
13#22582851—21no—
14#22582851—21no—
15C2×C4⋊Dic281—21no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×#17985117C2211yescharacteristic
18#22582813—21no—
19#22582812—21no—
20#22582801—21no—
21#22582800—21no—
22C22⋊#14555886C2211yescharacteristic
23#22582786—21no—
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27#17985137—42no—
28#17985137—42no—
29C2×Dic562—21no—
30C2×D1124D411yescharacteristic
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C22×Dic281—21no—
35C22×Dic281—21no—
36C22×Dic281D411yescharacteristic
37C22×Dic281D411yescharacteristic
38C2×C4×D281—21no—
39C2×#14555886—21no—
40C4⋊Dic281—21no—
41C4⋊Dic281—21no—
42C4⋊Dic281—42no—
43C4⋊Dic281D411yescharacteristic
44#17985117—21no—
45#17985117—21no—
46#17985117—21no—
47C22⋊Dic281—21no—
48#17985115—21no—
49#17985115—21no—
50C2×D4×C281—21no—
51C2×D4×C281D411yescharacteristic
52C22×C4×C281—21no—
53C22×C4×C281C2311yescharacteristic
54C2×C8×C281—21no—
55C4⋊C4×C281D411yescharacteristic
56C22⋊C4×C281—21no—
57C22×D281—21no—
58Dic562—42no—
59D1124—41no—
60C22⋊D281—42no—
61C22⋊D281—41no—
62C22⋊D281—41no—
63C22⋊D281—81no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C2×Dic281—21no—
68C2×Dic281—42no—
69C2×Dic281—41no—
70C2×Dic281—41no—
71C2×Dic281—41no—
72C2×Dic281—41no—
73C2×Dic281D812yes—
74C4×D281—42no—
75#14555886—41no—
76C23×C281—21no—
77C23×C281C2×D411yescharacteristic
78D4×C281—41no—
79D4×C281—41no—
80D4×C281—41no—
81C2×C4×C281—22no—
82C2×C4×C281—21no—
83C2×C4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281—41no—
86C2×C4×C281C2×D411yescharacteristic
87C2×C4×C281C2×D411yescharacteristic
88C8×C281—41no—
89C22×C281—21no—
90C22×C281—21no—
91C22×C281—41no—
92C22×C281—41no—
93C22×C281—41no—
94C22×C281#12011yescharacteristic
95C22×C281C2×D811yescharacteristic
96C22×C281AGL(1,ℤ/8)11yescharacteristic
97C2×D281—41no—
98C2×D281—41no—
99C2×D281—41no—
100C4×C281—21no—
101C4×C281—21no—
102C4×C281—42no—
103C4×C281—41no—
104Dic281—22no—
105Dic281—41no—
106Dic281—41no—
107Dic281—81no—
108C2×C281—21no—
109C2×C281—21no—
110C2×C281—81no—
111C2×C281#44711yescharacteristic
112C2×C281#45611yescharacteristic
113C2×C281#45811yescharacteristic
114D281—81no—
115C281#161011yescharacteristic, complemented, Sylow
116#1610—2811nomaximal, Sylow
117#537—2811no—
118#480—2811no—
119#480—2811no—
120#398—2811no—
121#327—2811no—
122#327D28111yescharacteristic, complemented
123#324—2811no—
124C2×#41—5621no—
125C22⋊Q8—5621no—
126C22⋊Q8—5621no—
127#121—2811no—
128#121—5621no—
129#121—5621no—
130#121—5621no—
131#121C2×D28111yescharacteristic
132C2×C4⋊C4—2811no—
133C2×C4⋊C4—2811no—
134C2×C4⋊C4—5621no—
135#107—5621no—
136#107—5621no—
137#102—5621no—
138#102—5621no—
139C22⋊C8—2811no—
140C22⋊C8C2×D28111yescharacteristic
141#95—5621no—
142#95C2×D28111yescharacteristic
143#41—11242no—
144#41—11242no—
145C2×Q8—5621no—
146C2×D4—21no—
147C2×D4—2811no—
148C2×D4—5621no—
149C2×D4—5621no—
150C2×D4—5621no—
151C2×D4D112411yescharacteristic
152C22×C4—21no—
153C22×C4—2811no—
154C22×C4—2811no—
155C22×C4—5621no—
156C22×C4—5621no—
157C22×C4—5621no—
158C22×C4C22×D28111yescharacteristic
159C2×C8—21no—
160C2×C8—5621no—
161C4⋊C4—2811no—
162C4⋊C4—5621no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4—11242no—
168C4⋊C4D112411yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—5621no—
171C22⋊C4—5621no—
172C22⋊C4—5621no—
173C23—21no—
174C23—5621no—
175C23D4×D28111yescharacteristic
176Q8—11242no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—11241no—
181D4—11242no—
182D4—11241no—
183D4—11241no—
184D4—22481no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2812no—
191C2×C4—5621no—
192C2×C4—5621no—
193C2×C4—5621no—
194C2×C4—5621no—
195C2×C4—11242no—
196C2×C4—11242no—
197C2×C4—11241no—
198C2×C4—11241no—
199C2×C4—11241no—
200C2×C4—11241no—
201C2×C4D4×D28111yescharacteristic
202C2×C4C2×D112411yescharacteristic
203C8—41no—
204C8—11241no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—11241no—
211C22—11241no—
212C22—11241no—
213C22#2258284911yescharacteristic
214C22D8×D28111yescharacteristic
215C22#2258290611yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—5622no—
221C4—11241no—
222C4—11241no—
223C4—22481no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—22481no—
228C2#3182359811yescharacteristic
229C2#3182364711yescharacteristic
230C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#31824040C2
hypercenter#327D281
hypocenterC281#1610
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #31823777C2semidirect
3. #31823774C2semidirect
4. #31823395C2semidirect
5. #31823196C2semidirect
6. #31823188C2semidirect
7. #327×C281C2semidirect
115. C281#1610semidirect
122. #327D281semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#318240402
#318237772
#318237742
#318233952
#318231962
#318231882
#327×C2812
#1610281